Problem: The sum of two numbers is $95$, and their difference is $61$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 95}$ ${x-y = 61}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 156 $ $ x = \dfrac{156}{2} $ ${x = 78}$ Now that you know ${x = 78}$ , plug it back into $ {x+y = 95}$ to find $y$ ${(78)}{ + y = 95}$ ${y = 17}$ You can also plug ${x = 78}$ into $ {x-y = 61}$ and get the same answer for $y$ ${(78)}{ - y = 61}$ ${y = 17}$ Therefore, the larger number is $78$, and the smaller number is $17$.